i'd recommend taking mostly light clothing (shorts, t-shirts) and definitly some formal wear. there are 2 formal evenings and the rest are called "smart casual" evenings. Formal night is in fact formal (some men wear tuxes, most wear suits). . Don't forget dress shoes as they do not sell them on board. I believe they have tux rentals from the passenger serivces desk if that is a better option for you. Ladies wear dresses, skirts, pantsuits. The second formal night is not as formal as the first so for example, a nice sundress is appropriate and a shirt and tie (no jacket) for men.
ladies: swimsuit, shorts x 4, tank tops x 4, t-shirtsx 3, nice blouse with skirt or dressx2 (one more dressy than other), 4 casual outfits, dress shoes or sandals, beach sandals, running shoes and gym clothes (if you want to use the gym onboard or for one of the tours) and something comfortable to walk around in.
men: same as above but bring casual pants (no shorts allowed in the dining rooms!) and don't forget the black/brown socks and a tie!!!
pack a swimsuit and essentials in a carry on bag as your luggage may take a while to get to your room (expect it 1 hour after the ship sails and you'll be pleasently surprised if it shows up earlier). . the room stewards work hard but they can't perform miracles!!! also, don't forget that airlines have this magic ability to lose luggage
hope this helps!!!